Hash Chemistry: Minimal Models for Evolutionary Growth of Complexity

2026-07-30

AI Summary

This study investigates the mechanisms underlying cross-scale open-ended evolutionary dynamics in minimal systems, with a focus on complexity growth and multiscale ecological interactions. Building upon the Hash Chemistry framework—wherein deterministic hash functions assign scalar scores to arbitrary entities to construct a combinatorially expansive possibility space—the work introduces spatial locality and binary competitive interactions into Structured Cellular Hash Chemistry (SCHC) for the first time. Leveraging GPU-accelerated large-scale spatial simulations and multiscale dynamical analysis, the research demonstrates that spatial scale acts as a control parameter capable of inducing nucleation-like phase transitions, thereby disentangling the distinct contributions of non-spatial size bias and finite spatial effects. The experiments reveal stochastic transitions from compact replicator states to size-dominated regimes, markedly enhancing evolutionary dynamics and affirming Hash Chemistry’s potential as a transparent testbed for open-ended evolution.

Abstract

Hash Chemistry is a family of minimalistic evolutionary models in which a deterministic hash function assigns a scalar score to entities of arbitrary size, opening a combinatorially vast possibility space (a ``cardinality leap''). Since its introduction, the idea has been realized in several settings, from the original spatial formulation to a fast non-spatial variant and then to structural cellular models. Here we review the Hash Chemistry family as a coherent modeling framework and use it to explore how minimal systems can demonstrate the mechanisms behind multiscale open-ended evolutionary dynamics. The most recent model, Structural Cellular Hash Chemistry (SCHC), successfully demonstrated multiscale ecological interaction/adaptation and complexity growth of replicators in a computationally efficient manner. In this study, we first extend SCHC to incorporate spatial locality and dyadicity of competitive interactions among replicating structures. We show this extension substantially enhances SCHC's evolutionary dynamics. Furthermore, we explore SCHC in a significantly larger spatial domain using a GPU-accelerated implementation. We show that the size of the space acts as a control parameter for a stochastic, nucleation-like transition between a compact-replicator regime and a runaway size-dominance regime, and we separate the responsible mechanism into a non-spatial, size-biased sampling feedback and a finite-size spatial effect. Altogether, these results illustrate the rich potential of Hash Chemistry as a minimal, mechanistically transparent testbed for studying open-ended evolution across scales.

Problem

• open-ended evolution
• complexity growth
• replicators
• spatial locality
• multiscale dynamics

Innovation

• Hash Chemistry
• open-ended evolution
• spatial locality
• multiscale dynamics
• GPU acceleration